Interpolation theorems for Lorentz martingale spaces

We apply function parameters, which was introduced by T.?F. Kalugina, to interpolation between martingale Hardy spaces. Some new interpolation theorems for Lorentz martingale spaces are proved.     

Interpolation theorem for Marcinkiewicz spaces with applications to Lorentz gamma spaces

This paper is devoted to the interpolation principle between spaces of weak type. We characterise interpolation spaces between two Marcinkiewicz spaces in terms of Hardy type operators involving suprema. We study general properties of such operators and their behavior on Lorentz gamma spaces. A particular emphasis is placed on elementary and comprehensive proofs.     

Factorization through Lorentz spaces for operators acting in Banach function spaces

Positivity - We show a factorization through Lorentz spaces for Banach-space-valued operators defined in Banach function spaces. Although our results are inspired in the classical factorization...     

Interpolation of Lorentz martingale spaces

In this paper,we apply function parameters,introduced by Persson,to real interpolation of Lorentz martingale spaces.Some new interpolation theorems concerning Lorentz martingale spaces are formulated.The results that we obtain generalize some fundamental interpolation theorems in classical martingale Hp theory.     

Lorentz spaces with variable exponents

We introduce Lorentz spaces and with variable exponents. We prove several basic properties of these spaces including embeddings and the identity . We also show that these spaces arise through real interpolation between and . Furthermore, we answer in a negative way the question posed in 12 whether the Marcinkiewicz interpolation theorem holds in the frame of Lebesgue spaces with variable integrability.     

Uncomplemented subspaces of Lorentz spaces

In the paper we construct a system of bounded functions which generates an uncomplemented subspace in the Lorentz space Λ(α) for all α∈(0,1). Lower bounds of the norms of the projector onto such subspaces are obtained. Translated fromMatematicheskie Zametki, Vol. 68, No. 1, pp. 57–65, July, 2000.     

Equivalent quasi-norms on Lorentz spaces

We give new characterizations of Lorentz spaces by means of certain quasi-norms which are shown to be equivalent to the classical ones.

     

Moser-type inequalities in Lorentz spaces

Moser-type estimates for functions whose gradient is in the Lorentz space L(n, q), 1q, are given. Similar results are obtained for solutions uH _inf0 ^sup1 of Au=(f _i ) _{x i} , where A is a linear elliptic second order differential operator and |f|L(n, q), 2q.Work partially supported by MURST (40%).     

Bilinear multipliers on Lorentz spaces

We give one sufficient and two necessary conditions for boundedness between Lebesgue or Lorentz spaces of several classes of bilinear multiplier operators closely connected with the bilinear Hilbert transform. The author has been partially supported by grants DGESIC PB98-1246 and BMF 2002-04013.     

Homogeneous Lorentz spaces. I

Sufficient conditions are obtained for maximality of the sequential order relation of events in Lorentz manifolds admitting a transitive group of motions.Translated from Ukrainskií Geometricheskií Sbornik, No. 30, 1987, pp. 116–122.     

Multidimensional rearrangement and Lorentz spaces

We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional properties of the associated weighted Lorentz spaces. This revised version was published online in June 2006 with corrections to the Cover Date.     

Homogeneous Lorentz spaces. 2

Translated from Ukrainskii Geometricheskii Sbornik, No. 31, pp. 112–117, 1988.     

Interpolation theorem on Lorentz spaces over weighted measure spaces

In 1997 Ferreyra proved that it is impossible to extend the Stein-Weiss theorem in the context of Lorentz spaces. In this paper we obtain an interpolation theorem on Lorentz spaces over weighted measure spaces.

     

The dual of noncommutative Lorentz spaces

We prove some noncommutative analogues of the classical results about dual spaces of the classical Lorentz spaces.     

Uniform convexity in Lorentz sequence spaces

Necessary and sufficient conditions for Lorentz sequence spacesd(a,p) (1<p<∞), to be uniformly convexifiable are given. In casep≧2 the modulus of convexity is calculated.